A Set and a Binary Operator are said to exhibit closure if applying the Binary Operator to two elements returns a value which is itself a member of .

The term ``closure'' is also used to refer to a ``closed'' version of a given set. The closure of a Set can be defined in several equivalent ways, including

- 1. The Set plus its Limit Points, also called ``boundary'' points, the union of which is also called the ``frontier,''
- 2. The unique smallest Closed Set containing the given Set,
- 3. The Complement of the interior of the Complement of the set,
- 4. The collection of all points such that every Neighborhood of them intersects the original Set in a nonempty Set.

© 1996-9

1999-05-26